摘要：The least absolute shrinkage and selection operator (LASSO) penalized regression is a state-of-the-art statistical method in high dimensional data analysis, when the number of predictors exceeds the number of observations. The commonly used Newton–Raphson algorithm is not very successful in solving the non-smooth optimization in LASSO. In this paper, we propose a fast generalized Newton–Raphson (GNR) algorithm for LASSO-type problems. The proposed algorithm, derived from a suitable Karush–Kuhn–Tucker (KKT) conditions based on generalized Newton derivatives, is a non-smooth Newton-type method. We first establish the local one-step convergence of GNR and then show that it is very efficient and accurate when coupled with a constinuation strategy. We also develop a novel parameter selection method. Numerical studies of simulated and real data analysis suggest that the GNR algorithm, with better (or comparable) accuracy, is faster than the algorithm implemented in the popular glmnet package.
关键词：LASSO; generalized Newton–Raphson; continuation; local one-step convergence; voting
